Integer optimization models of AI planning problems
The Knowledge Engineering Review
An approach to efficient planning with numerical fluents and multi-criteria plan quality
Artificial Intelligence
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
The FF planning system: fast plan generation through heuristic search
Journal of Artificial Intelligence Research
The 3rd international planning competition: results and analysis
Journal of Artificial Intelligence Research
PDDL2.1: an extension to PDDL for expressing temporal planning domains
Journal of Artificial Intelligence Research
Sapa: a multi-objective metric temporal planner
Journal of Artificial Intelligence Research
Taming numbers and durations in the model checking integrated planning system
Journal of Artificial Intelligence Research
The metric-FF planning system: translating "Ignoring delete lists" to numeric state variables
Journal of Artificial Intelligence Research
Journal of Artificial Intelligence Research
The deterministic part of IPC-4: an overview
Journal of Artificial Intelligence Research
An approach to temporal planning and scheduling in domains with predictable exogenous events
Journal of Artificial Intelligence Research
Loosely coupled formulations for automated planning: an integer programming perspective
Journal of Artificial Intelligence Research
On the use of integer programming models in AI planning
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Over-subscription planning with numeric goals
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Fast planning through planning graph analysis
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Processes and continuous change in a SAT-based planner
Artificial Intelligence
Cost-optimal planning with landmarks
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
An LP-based heuristic for optimal planning
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
The LAMA planner: guiding cost-based anytime planning with landmarks
Journal of Artificial Intelligence Research
Chance-Constrained Optimal Path Planning With Obstacles
IEEE Transactions on Robotics
COLIN: planning with continuous linear numeric change
Journal of Artificial Intelligence Research
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Although the use of metric uents is fundamental to many practical planning problems, the study of heuristics to support fully automated planners working with these fluents remains relatively unexplored. The most widely used heuristic is the relaxation of metric uents into interval-valued variables|an idea first proposed a decade ago. Other heuristics depend on domain encodings that supply additional information about fluents, such as capacity constraints or other resource-related annotations. A particular challenge to these approaches is in handling interactions between metric uents that represent exchange, such as the transformation of quantities of raw materials into quantities of processed goods, or trading of money for materials. The usual relaxation of metric fluents is often very poor in these situations, since it does not recognise that resources, once spent, are no longer available to be spent again. We present a heuristic for numeric planning problems building on the propositional relaxed planning graph, but using a mathematical program for numeric reasoning. We define a class of producer-consumer planning problems and demonstrate how the numeric constraints in these can be modelled in a mixed integer program (MIP). This MIP is then combined with a metric Relaxed Planning Graph (RPG) heuristic to produce an integrated hybrid heuristic. The MIP tracks resource use more accurately than the usual relaxation, but relaxes the ordering of actions, while the RPG captures the causal propositional aspects of the problem. We discuss how these two components interact to produce a single unified heuristic and go on to explore how further numeric features of planning problems can be integrated into the MIP. We show that encoding a limited subset of the propositional problem to augment the MIP can yield more accurate guidance, partly by exploiting structure such as propositional landmarks and propositional resources. Our results show that the use of this heuristic enhances scalability on problems where numeric resource interaction is key in finding a solution.